Search results for "Projection pursuit"
showing 3 items of 3 documents
PCA Gaussianization for image processing
2009
The estimation of high-dimensional probability density functions (PDFs) is not an easy task for many image processing applications. The linear models assumed by widely used transforms are often quite restrictive to describe the PDF of natural images. In fact, additional non-linear processing is needed to overcome the limitations of the model. On the contrary, the class of techniques collectively known as projection pursuit, which solve the high-dimensional problem by sequential univariate solutions, may be applied to very general PDFs (e.g. iterative Gaussianization procedures). However, the associated computational cost has prevented their extensive use in image processing. In this work, w…
Fast Estimation of the Median Covariation Matrix with Application to Online Robust Principal Components Analysis
2017
International audience; The geometric median covariation matrix is a robust multivariate indicator of dispersion which can be extended without any difficulty to functional data. We define estimators, based on recursive algorithms, that can be simply updated at each new observation and are able to deal rapidly with large samples of high dimensional data without being obliged to store all the data in memory. Asymptotic convergence properties of the recursive algorithms are studied under weak conditions. The computation of the principal components can also be performed online and this approach can be useful for online outlier detection. A simulation study clearly shows that this robust indicat…
Large-sample properties of unsupervised estimation of the linear discriminant using projection pursuit
2021
We study the estimation of the linear discriminant with projection pursuit, a method that is unsupervised in the sense that it does not use the class labels in the estimation. Our viewpoint is asymptotic and, as our main contribution, we derive central limit theorems for estimators based on three different projection indices, skewness, kurtosis, and their convex combination. The results show that in each case the limiting covariance matrix is proportional to that of linear discriminant analysis (LDA), a supervised estimator of the discriminant. An extensive comparative study between the asymptotic variances reveals that projection pursuit gets arbitrarily close in efficiency to LDA when the…